In X-ray computed tomography (CT), scattered radiation occurs as well as the primary radiation that is to be detected. If the detection of scattered radiation is not prevented, or if the recorded projections are not corrected, this leads to scattered radiation artifacts in the reconstructed CT volume, which consists of voxels. Such scattered radiation artifacts can, for example, be caused by a so-called cupping effect, which leads to unequal voxel values in a homogeneous object material, such that a curve rather than a straight line arises when the density values are applied along a line, so when a line profile is established. In addition, striped patterns and losses in contrast can generally occur. Scattered radiation also arises in the field of digital radiography and above all causes losses in contrast here.
There exist various known methods of resolution for scattered radiation correction, which can primarily be separated into two groups:    1. Measures for the reduction in detected scattered radiation, such as is carried out, for example, by using an anti-scatter grid.    2. So-called a posteriori corrections of the scattered radiation by subtracting the scattered proportion accordingly in each CT projection.
For the second group, it is necessary to have as accurate a knowledge as possible of the detected scattered proportion. For this, various approaches exist for determining this scattered proportion, which can also be separated into two groups:    1. Software-based solutions, which can be, for example, Monte Carlo simulations, deterministic calculations of first-order scattering, convolution algorithms based on so-called point spread functions.    2. Experimental methods for determining the scattered proportion by measurements.
Within this second group of experimental methods, different measuring procedures are known. For example,    a) beam-stopper-based methods and    b) a technique that is complementary thereto, which uses apertures and even so-called beam holes, and    c) a method that has only been proposed recently, which is based on so-called primary modulation.
As regards the most recent method, the following related art is known.
U.S. Pat. No. 7,463,712 B2 discloses scattered radiation correction for the generation of an X-ray image, wherein a direction-dependent modulation of the primary X-rays is used, which leads to a location-dependent modulation on the detector of the primary radiation. Scattered radiation in an X-ray image generation system having an X-ray source and an X-ray detector is corrected by using amplitude modulation for translating the spatial frequency of a detected X-ray to a higher frequency and by filtering out the low-frequency scattered radiation. One way to obtain the low-frequency primary signal without scattered radiation is by demodulation.
The decisive advantage of a method that uses primary modulation over many other known experimental methods is that the scattering measurement and scattered radiation approximation can hereby be carried out within the actual CT scan, i.e. the scattered data is extracted at the same time as the actual CT projections. Compared to other known methods, which require an additional measuring process, this leads to less measuring expenditure and at the same time to time being saved, which represents a decisive improvement for X-ray CT in particular. In addition, radiation dosage is also saved compared to measuring methods wherein an additional measuring process is required.
The method disclosed according to U.S. Pat. No. 7,463,712 B2 is based on a spatial primary modulation. As a result of high image frequencies, which are caused in particular by hard transitions in the image caused by edges of the object to be recorded, there arises in the frequency domain an overlap of the spectral copy of the primary information with the unmodulated frequency information. This renders a clean demodulation of the primary image more difficult. This problem is partially solved by a proposed, so-called “boundary detection”. Furthermore, in the maximum resolvable (image) frequency for the reconstruction of the primary image, and thus also for that of the scattered image, one is limited by the fixed, spatial modulator frequency. The maximum image frequency that can be reconstructed for the scattered image thus lies at half the modulator frequency. An unmoved primary modulator that is used here often leads to ring artifacts in the reconstructed CT volumes.
The known method according to U.S. Pat. No. 7,463,712 B2 provides that a primary modulator is placed between the object to be recorded and X-ray tubes. The primary modulator imprints a pattern onto the primary rays by amplitude modulation, for example in the form of a chess-board with light and dark fields. To that end, a circuit board made from copper can be used, for example, into which a pattern is introduced by an etching process, i.e. the copper is etched away accordingly on the light fields. The attenuation properties or attenuation coefficients of copper or of the bare circuit board material, which have different strengths, ensure a corresponding radiation attenuation through the dark fields (copper), whereas hardly anything or nothing at all (as regards circuit board material) is attenuated on the light fields. During the entire CT scan or the entire CT scanning, the modulator is located in a stationary, i.e. unmoved, position between the object and X-ray tube, i.e. it does not change its position. The modulated, chess-board-like pattern is thus to be found again in every projection of the CT scan, i.e. both in the radiation region and in regions covered by the object. Here, the relative modulation strength that addresses the primary signal is the same size at all positions. However, it is not only this modulated primary signal that is recorded by the detector, but this is also superimposed by an unmodulated, spatially low-frequency scatter signal, which comes about as a result of X-ray scattering effects, in particular Compton scattering processes, in the test object and in the laboratory environment. The detector therefore receives a complete signal formed by the modulated primary signal and the superimposed, unmodulated scattering signal.
It is hereafter possible to separate the modulated primary signal in the Fourier space from the unmodulated scattering signal. This takes place via a corresponding high-pass or low-pass filtering of the modulated projection. In the frequency domain, the low-pass-filtered version of the modulated projection results in the superimposition of the frequency proportions of unmodulated primary image and scattering function. The high-pass-filtered version contains only the spectral components of the modulated primary signal, so can later be demodulated and weighted so as to obtain an approximation of the sole primary signal in the frequency domain. After inverse Fourier transformation, this can be subtracted as an approximated primary image of the low-pass-filtered version, which has scattering and primary signals, so as to obtain an approximation of the scattered image. It is noted that, in the method described herewith, a so-called edge detection and edge smoothing are applied to each modulated projection, which is also described as boundary detection. Such a smoothing considers that high-frequency image proportions are already present as a result of the object alone and in particular due to the object edges. This is independent of each modulation. These high-frequency, unmodulated proportions overlap with the spectral copies of the modulated primary signal in the Fourier space. Mixing modulated and unmodulated signals has, as a consequence, an incorrect demodulation of the primary signals if this is not corrected. This means that, in particular in the object edge regions and also in the interior of the object, which is then described in this context as “spilling”, it leads to artifacts and a false reconstruction of the primary image. These effects also have an effect on the scattered image generated later. To absorb or suppress such high-frequency image proportions, which are in particular caused by object edges, the so-called boundary detection is applied, which finds object edges and smoothes them accordingly using a Gaussian filter. The significant artifacts caused by the high-frequency, unmodulated image proportions, are indeed hereby reduced; however, there arises imprecision in the edge region at such points, since the Gaussian filter is later rendered no longer retrogressive. The scattered image extracted in this way is now correspondingly removed from the CT projections. Since the modulation pattern is now still present in the projections, the CT projections are normalized to the radiation intensity according to the modulator. In this way, the modulator pattern in the projection image can then be removed. This takes place using division by recording the modulator without further objects in the beam path. Such a recording can also be described as reference measurement. It is noted that beam-hardening effects occur as a result of the modulator and indeed in particular due to the dark copper fields. If such effects remain uncorrected, there first arises an erroneous scattering approximation and then an incomplete removal of the chess-board pattern in the last-mentioned division step. Due to the stationary modulator, this can have ring artifacts in the CT cross-sectional images as a consequence. The fact that beam-hardening effects exist and lead to the cited errors is, for example, known from “Korrektur von Strahlaufhärtungsartefakten bei der Computertomographie” (Correction of beam-hardening artifacts in computed tomography) by Peter Hammersberg and Mans Mangard in the Journal für Röntgen-Wissenschaft and Technologie 8 (Journal for X-ray science and technology, volume 8), IOS Press, 1998, pages 75-93.
Hammersberg and Mangard disclose that exact density measurements are rendered more difficult during the use of polyenergetic X-ray sources as a result of beam hardening based on erroneous gradients of linear attenuation coefficients in computed tomography cross-sectional images. A corrective method is described wherein polyenergetic computed tomography data is converted into monoenergetic computed tomography data. Computed tomography data is derived as a function of the object thickness from measured data points and is depicted as a polynomial. The polyenergetic computed tomography data is simulated exactly by simulation based on the object material density, the object material composition, the X-ray energy spectrum, the detector response and the information transfer from the detector to digitalized data. The curved line of the function representing the polyenergetic computed tomography data can be determined exactly by a polynomial to the eighth order or higher, or by cubic spline interpolation.